Uniqueness of meromorphic functions that share three values
type: Item
instance of: scholarly article
title: Uniqueness of meromorphic functions that share three values
zbMATH Open document ID: 0767.30026
author: Shouzhen Ye
published in: Kodai Mathematical Journal
publication date: 1993-05-16T00:00:00Z
review text: The author proves the following theorem on shared values of meromorphic functions. Theorem. Let \(f\) and \(g\) be two distinct nonconstant meromorphic functions such that \(f\) and \(g\) share 0, 1, \(\infty\) with the same multiplicities (i.e. C.M.), and let \(a_ 1,a_ 2,\dots,a_ p\) be \(p\) (\(\geq 1\)) distinct finite complex numbers, and \(a_ i\neq 0\) (\(i=1,2,\dots,p\)). If \[ \sum_{i=1}^ p f(a_ i,f)+f(\infty,f)>{{2(p+1)} \over {p+2}}, \] then there exists one and only one \(a_ j\) in \(a_ 1,a_ 2,\dots,a_ p\) such that \(a_ j\) and \(1- a_ j\) are Picard exceptional values of \(f\) and \(g\) respectively, and also \(\infty\) is so, and \[ (f-a_ j)(g+a_ j-1)\equiv a_ j(1-a_ j). \] {}.
reviewed by: Fred Gross
Mathematics Subject Classification ID: 30D30
Mathematics Subject Classification ID: 30D35
zbMATH DE Number: 167942
zbMATH Keywords: shared values
zbMATH Keywords: Picard exceptional values
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138039600
OpenAlex ID: W2055293514
cites work: Meromorphic Functions that Share Three or Four Values
cites work: Q5723337
cites work: Unicity theorems for meromorphic or entire functions
cites work: Q3477118
cites work: Q5683031
DOI: 10.2996/KMJ/1138039600
description: scientific article; zbMATH DE number 167942